What is implicit (dy)/(dx),y=(sin(x))^{6x} ?

The answer to implicit (dy)/(dx),y=(sin(x))^{6x} is (dy)/(dx)=6sin^{6x}(x)(ln(sin(x))+xcot(x))

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implicit (dy)/(dx),y=(sin(x))^{6x}

implicit derivative

\frac{d y}{d x}, y = (sin (x))^{6 x}

\frac{d y}{d x} = 6 sin^{6 x} (x) (ln (sin (x)) + x cot (x))

Solution steps

y = (sin (x))^{6 x}

Treat

y

y (x)

Differentiate both sides:

\frac{d y}{d x} = 6 sin^{6 x} (x) (ln (sin (x)) + x cot (x))

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = 6 sin^{6 x} (x) (ln (sin (x)) + x cot (x))

\frac{d y}{d x} = 6 sin^{6 x} (x) (ln (sin (x)) + x cot (x))

\frac{\partial}{\partial x} (x^{2} + y^{2} - 9)

\int sec^{2} (2 x t a) n^{6} 2 x d x

\frac{d}{d x} (\frac{3}{x} + e^{2 x} \cdot 2)

f (x) = x^{2} - 3, (2, 1)

n = 0 \sum \infty \frac{n + 1}{3}

What is implicit (dy)/(dx),y=(sin(x))^{6x} ?
The answer to implicit (dy)/(dx),y=(sin(x))^{6x} is (dy)/(dx)=6sin^{6x}(x)(ln(sin(x))+xcot(x))